Fuzzy Logic Control Using Matlab Part II Naveed Ahmed, FAST-NUCES, Lahore.

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1 Fuzzy Logic Control Using Matlab Part II Naveed Ahmed, FAST-NUCES, Lahore. This 2-day workshop was held under the auspices of the Khwarzimic Science Society at the University of Lahore in April Full details and copies of this document can be obtained from Building Systems with the Fuzzy Logic Toolbox Although it s possible to use the Fuzzy Logic Toolbox by working strictly from the command line, it is easier to build the system using graphical user interface. There are five primary GUI tools for building, editing, and observing fuzzy inference systems in the Fuzzy Logic Toolbox: the Fuzzy Inference System or FIS Editor, the Membership Function Editor, the Rule Editor, the Rule Viewer, and the Surface Viewer. The FIS Editor handles the high level issues for the system: How many input and output variables? What are their names? The Membership Function Editor is used to define the shapes of all the membership functions associated with each variable. The Rule Editor is for editing the list of rules that defines the behavior of the system. The last two GUIs are used for looking at, as opposed to editing, the FIS. The Rule Viewer is a MATLAB-based display of the fuzzy inference diagram. Used as a diagnostic, it can show which rules are active, or how individual membership function shapes are influencing the results. Surface Viewer can display how one of the outputs depends on any one or two of the inputs- that is, it generates and plots an output surface map of the system. The five principal GUI editors all exchange information, if appropriate. Any one of them can read and write both to the workspace and to the disk. For any fuzzy inference system, any or all of these five editors may be open. If more than one of these editors is open for a single system, the various GUI windows are aware of the existence of the others, and will, if necessary, update related windows. Getting Started The Basic Tipping Problem. Given a number between 0 and 10 that represents the quality of service at a restaurant (where 10 is excellent), what should the tip be? The starting point is to write down the three rules for tipping, based on our personal experience. 1. If the service is poor then tip is cheap 2. If the service is good then tip is average 3. If the service is excellent then tip is generous Now that we have got the rules, we can start working with the GUI tools. The FIS Editor When creating a new fuzzy inference system for scratch, the place to start is the FIS Editor. To do that type fuzzy, this will call up a window that acts as the high-level view of a FIS. The system that is displayed is a default start-up system, since we didn t specify any particular system. You can either build a new system from scratch or you can load the already built system by typing fuzzy tipper1.

2 The FIS Editor displays general information about a fuzzy inference system. Default system already has one input and one output. We will change their names according to our tipping problem. The next thing to do is to define the membership functions associated with each of the variables. To do this, we need to open up the Membership Function Editor by pulling down the View menu item and selecting Edit Membership Functions. The Membership Function Editor The Membership Function Editor shares some features with the FIS Editor. In fact, all of the five basic GUI tools have similar menu options, status lines, and Help and Close buttons. The Membership Function Editor is the tool that lets you display and edit all of the membership functions for the entire fuzzy inference system, including both input and output variables.

3 The Rule Editor The Rule Editor contains a large editable text field for displaying and editing rules. You can use Add Rule Button to add new rules to the fuzzy inference system. After the system has been completely defined: you ve got the variables, membership functions, and rules necessary to calculate tips. It would be nice, at this point, to look at a fuzzy inference diagram like one at the last page of previous lecture notes and verify that every thing is behaving the way it should. This is exactly the purpose of Rule Viewer. From the View menu, select View Rules. The Rule Viewer The Rule Viewer displays a road map of the whole fuzzy inference process. Each rule is a row of plots, and each column is a variable. So the first column of plots ( the three yellow plots) shows the membership functions references by the antecedent, or if-part, of each rule. The second column of plots (the three blue plots) shows the membership functions references by the consequent, or then-part of each rule. There is a yellow index line across the input variable plots that you can move left and right by clic king and dragging with the mouse. This changes the input value. When you release the line, a new calculation is performed, and you can see the whole fuzzy inference process take place before your eyes.

4 Finally the aggregation occurs down the second column, and the resultant aggregate plot is shown in the single plot to be found in the lower right corner of the plot field. The thick line passing through the aggregate fuzzy set shows the defuzzified output value. With Rule Viewer you can take in the whole fuzzy inference process in one sweeping view. The Rule Viewer is very good, for example, at showing how the shape of certain membership functions is influencing the overall results. The Rule Viewer shows one calculation at a time and in great detail. If you want to see the entire output surface of your system, that is the entire span of the output set based upon the entire span of input set, you need to open up surface viewer. You can open it by selecting View Surface. from the View menu. The Surface Viewer Upon opening the Surface Viewer, we are presented with a two dimensional curve that represents the mapping from service quality to tip amount. Since this is a one-input one-output case, we can see the entire mapping in one plot. Two input one-output systems also work well, as they generate three-dimensional plots that MATLAB can adeptly manage. But when we move beyond three dimensions overall, we start to encounter trouble displaying the results. Accordingly, the Surface Viewer is equipped with pop-up menus that let you select any two inputs and any one output for plotting. Pushing the Evaluate button initiates the calculation, and the plot comes up soon after the calculation is complete. If you have got two inputs and one output the output surface would be like the figure on right. FIS Evaluation in Matlab To evaluate the output of a fuzzy system for a given input, use the function evalfis. Write the following code upto evalfis and pres enter, to get answer. a = readfis('tipper') evalfis([1 2], a) ans = This function can also be used for multiple collections of inputs, so each row of the input matrix is a different input vector. By doing multiple evaluations at once, you get a tremendous boost in speed. evalfis([3 5; 2 7], a) ans =

5 FIS Evaluation in C In the fuzzy/fuzzy directory of the toolbox, you can find two C files, fismain.c and fis.c, which are provided as the source codes for a stand-alone fuzzy inference engine. The stand-alone fuzzy inference engine can read a FIS file and an input data file to perform fuzzy inference directly, or it can be embedded in other external applications.